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State-space models are successfully used in many areas of science,engineering and economics to model time series and dynamical systems. Wepresent a fully Bayesian approach to inference \emph{and learning} (i.e. stateestimation and system identification) in nonlinear nonparametric state-spacemodels. We place a Gaussian process prior over the state transition dynamics,resulting in a flexible model able to capture complex dynamical phenomena. Toenable efficient inference, we marginalize over the transition dynamicsfunction and infer directly the joint smoothing distribution using speciallytailored Particle Markov Chain Monte Carlo samplers. Once a sample from thesmoothing distribution is computed, the state transition predictivedistribution can be formulated analytically. Our approach preserves the fullnonparametric expressivity of the model and can make use of sparse Gaussianprocesses to greatly reduce computational complexity.

Bayesian Inference and Learning in Gaussian Process State-Space Models with Particle MCMC